| Description of Earth or Material. Earth upon Earth. | Coefficient of Friction during Motion—F. | Corresponding Slope. S TO 1 = 1 F. |
|---|---|---|
| Damp vegetable or loamy earth | 0·50 to 0·67 | 2 to 1 TO 1½ to 1 |
| Clean dry shingle or ballast, nearly without sand | 0·75 to 0·80 | 1⅓ to 1 TO 1¼ to 1 |
| Clean wet shingle or ballast, nearly without sand | 0·67 | 1¼ to 1 |
| Shingle or ballast with ordinary quantity of sand | 0·80 | 1¼ to 1 |
| Note.—The presence of sand in gravel increases the frictional resistance because it makes it gritty. | ||
| Excavated hard road metalling, cast into a mound | 0·80 | 1¼ to 1 |
| Fine dry sand | 0·75 | 1⅓ to 1 |
| Hard clay, slightly damp | 0·67 | 1½ to 1 |
| Hard clay, damp to wet | 0·40 to 0·50 | 2½ to 1 TO 2 to 1 |
| Damp lias, yellow, and most upheaved clays in superficial beds | 0·25 to 0·33 | 4 to 1 TO 3 to 1 |
| Wet rubble on wet rubble, ordinary size and character | 0·67 to 0·80 | 1½ to 1 TO 1¼ to 1 |
| Do., do., when the surfaces are unclean | 0·67 | 1½ to 1 |
| Do., do., Large to very large size. Surfaces clean | 0·80 to 1·0 | 1¼ to 1 TO 1 to 1 |
| Note.—All rubble carefully deposited. | ||
| Rough-faced granite on gravel and sand, both dry | 0·54 | 1·85 to 1 |
| Rough-faced granite on gravel and sand, both wet | 0·48 | 2·09 to 1 |
| Rough-faced granite on sand, both dry. | 0·70 | 1½ to 1 |
| Rough-faced granite on sand, both wet | 0·53 | 1·88 to 1 |
| Constructed Material on Earth. | ||
| Rubble masonry, or brickwork on clay, dry | 0·50 | 2 to 1 |
| Rubble masonry, or brickwork on clay, wet | 0·33 | 3 to 1 |
| Note.—Vide Chapter II. |
Friction is the chief cause of stability in granular soils and those readily affected by moisture which have for practical purposes no immutable cohesion. In few earths are both cohesion and friction of considerable and reliable value, one or the other quickly becoming impaired or destroyed. Movement is caused by such various means that each earth must be separately considered, and also the circumstances under which it is placed. The particles of the earth may be dissolved by water and become in a muddy state, or they may be considered insoluble as in clean sand and gravel, although in compact sand or gravel the cementing material may crack and weather. Provided it was certain any earth would always remain as originally formed, a condition which it is impossible to guarantee in work, the cohesion and frictional resistance being known, the correct slope could be mathematically determined, but as all earths are subject to varying deteriorating influences, such a deduction is only valuable as a guide for reasonable inference. Cohesion may be more quickly impaired by certain action than friction, and vice versâ. Probably, of all soils, that to be most distrusted is one that expands and contracts, such as clay earth, which although possessing considerable cohesion may become upon drying a mere congregation of disconnected lumps ready to move upon the return of wet weather, thus its considerable power of cohesion may practically be one of the chief causes of a slip. On the contrary, clean sand, although devoid of cohesion, will not crack or have a greasy surface, but the particles may be washed away.
To ascertain that any earth is uniformly affected throughout the mass, and to prevent or provide against deteriorating influences is the chief aim. It is useless to declare any earth possesses considerable cohesion when the power can be quickly dissipated by ordinary atmospheric action and even become a cause of movement, and to rely for permanent stability upon such property. In ordinary earths, not rock, it will generally be found that cohesion is small or insignificant in soil having a coefficient of friction of some moment, and the reverse. In most earths friction, although it is affected in a greater degree by vibration, has to be relied upon, and not cohesion, as the latter is variable and may exist almost unimpaired in a lump, which nevertheless may become detached because of fissures. The coefficients of friction of different earths are also better known than the cohesion; but how easily even friction is impaired may be gathered from the sudden manner in which bridge cylinders will sink after having hung for days by surface friction, or been held by the transitory expansion of clay. Mr. Wilfrid Airy, B.A., in a series of experiments on the cohesion of earth, found that in strong brick loam it is about 168 lbs. per square foot, in compact clay and gravel it may reach 800 lbs. per square foot of section, and in clean sand it is practically nihil.
In rock the slope of repose depends whether the earth is unstratified or stratified; and if stratified, upon the dip of the strata and their resistance to the effects of the weather. A vertical face may be stable in unstratified or stratified rock, provided in the latter case it does not dip towards a cutting; or the requisite slope may range from ¼ to 1 to such an inclination that the cohesion and friction, which vary greatly, are sufficient to prevent movement. In sidelong ground should the rock dip parallel to the surface the hill slope may require to be flat, whereas the valley slope may stand vertically.
Although, perhaps, in many instances the slopes of cuttings and embankments have been arbitrarily fixed, it may be said, on the whole, no very serious interruptions to traffic have been caused from the sole want of sufficient initial flatness of a slope, as that will soon become known. In determining the inclination it is not the angle at which the earth will stand at the time of excavation or deposition, and for a few months after that is required to be ascertained, but that which will permanently suffice to prevent movement. It is well known that almost all freshly cut soil stands nearly vertically for a small depth for a few days in ordinary weather but then begins to crumble and finally break away.
What then will be the slope of permanent stability? This chiefly depends upon the degree of exposure, the effects of the weather, water, and vibration upon the soil, and the depth or height of a cutting or embankment.
Each earth requires to be duly considered; for instance, gravel and sand are pieces of rock, however small, and for earthwork purposes the particles may be regarded as insoluble in water; nevertheless in the case of sand, should it be charged with water, it may be necessary to treat it as a fluid, the same as mud, although water does not change the particles; however, slips in cuttings and embankments in sandy or gravelly soils are not usually caused by their becoming gradually saturated throughout their mass, but by a flow of water which creates water seams: the stability, therefore, is dependent upon equal percolation and drainage and protection of the surface; and the slope that should be given to a sand cutting is also governed by the quantity of water it will have to hold, and whether the sand is pure or loamy. The depth of a cutting in sand has a considerable influence upon the slope of stability, for frequently sand is in a dry state in the upper portion of a cutting, but beneath it is wet, and partakes more of a silty character, and therefore may stand at a steeper inclination in the upper part, but require a flat slope in the lower portion. The same conditions are found in all soils, and the sides of a cutting vary, one may be comparatively compact and free from water, the other in a wet state and disintegrated. They will not permanently repose at the same angle, the slope varying according to the degree of dryness, size, and uniformity of the particles. In all earths in which cohesion is liable to be quickly destroyed, a straight slope is the best as having an even surface, which prevents the formation of depressions and causes the water to drain away, and also offers the least surface to the weather. In all earth such as shingle, gravel, or sand, consisting of pieces of rock or rubble, or having round particles, it is important to remember that any surface disturbance may cause serious movement, particularly should it commence at the bottom of a slope, as then the revolving action may not cease until a flatter inclination is produced by material rolling from the top and not reposing until it nearly reaches the base. The quantity of moisture is the chief governing condition of the slope of repose in clay soils, and it should not be forgotten that this may vary considerably. Clay when only slightly moist may stand at a 1 to 1 or 1½ to 1 slope, but as it gradually becomes in a wet state will require a flatter inclination, and may not be at rest until the slope is at least 3 to 1, and it is not safe to rely upon a steeper slope than 3 to 1 in the case of almost any surface clay beds liable to become charged with water, and even 4 to 1, should the excavation be on the side of a clay hill and near houses, or the ground be loaded; but clay having some powers of cohesion which usually are greater as the clay is harder, is not so quickly disintegrated as in the case of more porous soil, and the form of the slope it assumes is not a straight line; that most usually approached by sand or gravel or a granular soil consisting of particles of the same character, although the lower part of the slope may be flattened consequent upon the erosion of the finer particles which crumble and become deposited at the base.
As a rule, the greater the cohesion of the soil the more curved is its natural slope, the greatest pressure being at the base where the inclination is flatter, and is steeper towards the top, as the ground may be held together by cohesion at a vertical face. The harder and looser the particles the straighter will be the slope, and if the ground gradually increases in firmness it will usually be nearly straight; but if the contrary condition exists, the natural slope will be flatter towards the base although nearly vertical for a few feet from the top.
As a proof how quickly clay becomes less stable and loses its cohesive power with the usual quantity of moisture in it, when first tipped it may assume a slope of 1 to 1 TO 1½ to 1, but upon exposure to the weather, which causes the lumps to waste away and the clay to swell from moisture and other agencies, the firmest clay in cuttings and embankments may be said to be unstable until a slope of at least 1½ to 1 is reached in moderate depths, and 2 to 1 TO 3 to 1 in high embankments or deep cuttings. In all earths the chief cause of movement of earth is water, and the main questions to be decided are so far as regards the inclination of the slope.
1. Should the surfaces of a cutting be drained and protected and be excavated to a comparatively steep slope; or,